Question

A siren blown in workshop emits waves of frequency1000 Hz A car driver approaches the workshop withvelocity 90 km/hour then frequency of sound heard bydriver will be in Hz. [SPET 911​

Answer 1

A car driver approaches the workshop which emits waves of frequency 1000 Hz, with a velocity of 90 km/hour then the frequency of sound heard by driver will be is 1081.96 Hz.

Explanation:

The frequency of the waves emitted from the siren in the workshop, f = 1000 Hz

The velocity of the car, v = 90 km/hr = 90 * [5/18] m/s = 25 m/s

Now,  

The frequency of the sound of the waves heard by the driver while approaching the workshop is given by,

fo = $\frac{f * c}{c - v}$ ….. (i)

where

fo = observed frequency i.e., frequency of the sound heard by the driver

f = frequency of the source i.e., frequency of the waves from the siren

c = velocity of sound in air = 330 m/s

By substituting the given values in eq. (i), we get

fo = (1000 × 330) / (330 - 25)

⇒ fo = 330000 / 305

⇒ fo = 1081.96 Hz

Thus, the frequency of sound heard by the driver will be 1081.96 Hz.

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Answer 2

Given:

1. Frequency of siren wave = 1000Hz
2. Velocity of car driver = 90 km/h
3. speed of sound waves = 330 m/s

To find:

1. Frequency of sound heard by the driver

Solution:

The given question can be solved by using the doppler effect as follows:

The equation for the dopplers effect can be given as:

f₀ = $f_{s}$ ( $\frac{v + v_{0} }{v + v_{s} }$)

1. $f_{o}$= observer frequency of sound
2. v = speed of sound waves
3. $v_{o}$= observer velocity
4. $v_{s}$=source velocity
5. $f_{s}$ = actual frequency of sound waves

The frequency of the sound of the waves heard by the driver while approaching the workshop can be given by putting the given values in the equation as follows:

90 km/ h = 25 m/s

fo = 1000 ( 25 +330) / (330)

fo = 1076 Hz

Thus, the frequency of the sound heard by the driver will be 1076 Hz.